Question

If the roots of x²+mx+12=0 are in the ratio 1:3,then find m.

Answer 1

let the roots of the equation be 'a' and 'b'
a/b=1/3
therefore
b=3a
product of the roots=ab=constant /coeff of x sq.
=ab=12/1
=3$a^{2}$=12
$a^{2}$=4
a=+/-2
wen a=2,b=6
wen a=-2,b=-6
sum of the roots= -coeff of x/coeff of x sq.
=a+b=-m/1
=+/-8
ans m=+/-8
(+/-2)

Answer 2

Let the roots are x and 3x
we know that sum of roots = -b/a
⇒x +3x = -m 
⇒4x = -m
and product of roots = c/a
⇒3x² = 12
⇒x²= 4
⇒x = 2 or -2
so,when x =2, m = -8
when , x= -2 , m =8